Two consecutive odd integers have a sum of 152, what are the integers?

Jan 31, 2016

If the odd integers are consecutive, call one $' n '$ and the other $' n + 2 '$. Solving the equation yields $n = 75$ and $n + 2 = 77$.

Explanation:

If we call the first of the two integers $' n '$ , then the odd number immediately after it ('consecutive') is $' n + 2 '$. (because there's an even number in between)

We realize that the numbers are going to be somewhere around 75, since when added together they yield something around 150. This kind of estimation is helpful for thinking about whether the answer we come up with makes sense.

We know:

$n + \left(n + 2\right) = 152$

$2 n + 2 = 152$

$2 n = 150$

$n = 75$

So the first of our numbers is $75$, and the other is the next odd number, $77$.